4/5x+3=2/4x-9

Solution for 4/5x+3=2/4x-9 equation:

4/5x+3=2/4x-9

We move all terms to the left:

4/5x+3-(2/4x-9)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 4x-9)!=0

x∈R


We get rid of parentheses

4/5x-2/4x+9+3=0

We calculate fractions


16x/20x^2+(-10x)/20x^2+9+3=0

We add all the numbers together, and all the variables

16x/20x^2+(-10x)/20x^2+12=0

We multiply all the terms by the denominator


16x+(-10x)+12*20x^2=0

Wy multiply elements

240x^2+16x+(-10x)=0

We get rid of parentheses

240x^2+16x-10x=0

We add all the numbers together, and all the variables

240x^2+6x=0

a = 240; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·240·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6}{2*240}=\frac{-12}{480}
=-1/40
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*240}=\frac{0}{480}
=0
$